In developing or assessing the performance of control systems there are instances where complex mathematical operations must be performed. In many cases, these operations include calculus and Laplace or Fourier transforms not routinely used by many control engineers.

In these cases, users must dust off old textbooks and review how to perform these operations and then execute what can be laborious conversions and calculations. Often, when doing mathematical operations one may not routinely perform, there exists increased possibility of error forcing multiple rechecks.

One alternative to laborious review and manual execution of required math functions is a software package from Wolfram Research (Champaign, Ill.) that not only aids in tutoring but also in performing the operations. Wolfram Research's Mathematica 4 addresses these issues by providing a wide scope of mathematical knowledge and capability.

Graphic images created by Mathematica 4 can be cut and pasted into other software applications.

Included in Mathematica 4 is the capability to perform a range of operations applicable to control system implementation and support. Among these are:

• Basic computations;
• Algebra including curve fitting;
• Integral and differential calculus;
• Laplace and Fourier transforms;
• Plotting and graphing.

Mathematica 4 comes with a CD that contains software, online help files, and hard copies of manuals that outline the purpose and format of the commands under the software.

The help files include a browser that indexes content by function or alphabetically, and allows key word searches. Also in the help files is an electronic version of the reference book, The Mathematica Book, 4^th edition by Stephen Wolfram, Wolfram Media/Cambridge University Press 1999. This book provides easy access to understanding command purpose, formats, and results.

Wolfram Research is careful to warn users that the software is not a replacement for basic understanding of the mathematical principles being applied. Rather, it's a tool to increase productivity through its speed and accuracy in performing functions for the knowledgeable user. Mathematica 4 is a powerful but complex product that must be approached with knowledge and respect.

Before launching into Mathematica 4, its developer strongly advises going through the basic examples provided in a Getting Started manual. This is extremely helpful in giving users the basics to enter functions, because formatting commands, variables, and the use of brackets must be thoroughly understood.

As a second step before performing an operation for a specific application, it is strongly advised to test the desired function or one with a known solution in one of the examples. This is to assure that command application or formatting errors are not present.

Once formulas are input, the package quickly provides the result in text or graphic format. Both the input and resulting output can be cut and pasted into other Microsoft Windows applications. For example, note the following calculus example from the example problem set:

Input function:

Resulting output function:

As an additional help to formula input, Mathematica 4 includes toolboxes referred to as 'palettes.' These palettes allow point-and-click function selection, which aids the user in remembering command wording and allows direct symbol input, lessening typographical errors.

Mathematica 4 runs under Microsoft Windows 95, 98, and NT as well as Mac OS, Linux (Intel), and other operating systems.

For more information on Mathematica 4, visit www.controleng.com/freeinfo.